Message #688

From: "anthony.deschamps" <anthony.deschamps@yahoo.ca>
Subject: A description of my 5D cube solution
Date: Fri, 09 Oct 2009 02:37:26 -0000

My name is Anthony Deschamps. I am 17 years old and living in Windsor, Ontario, Canada. I am in my last year of high school, and next year I plan to study physics, chemistry or something in between. I recently became the 20th person to solve the 3^5 cube and I thought I’d explain the general strategy that I used to solve it. This isn’t a complete description of my solution, but rather a description of the concepts I used to come up with the solution.

I think the biggest challenge when solving higher dimensional cubes is realizing that the fourth dimension and beyond are really no different from the first three that we are so familiar with. Most, if not all of the same algorithms you would use in 3D still apply and are quite useful.

It also helps if your solution to the 3D cube is more logic based rather than consisting of memorized sequences. I use a number of algorithms that are based on the same idea: Pick a side of the cube and do whatever you need to do in order to manipulate one or two pieces while leaving the rest of the side untouched. Now you can turn that side and perform everything you just did in reverse, which will restore any damage you did to the rest of the cube. Now turn that side back to where it was and you’re done. This method can be used to swap two pairs of corners/edges or to rotate one corner clockwise and another counter clockwise.

If you don’t solve the 3D cube like this (I know there are faster ways, like the Fridrich method) I would recommend trying it in order to get the hang of it. It gives you a finer degree of control. Besides, it’s useful for making patterns on the cube, if you enjoy that sort of thing.

Moving on to the 5D cube, my solution went something like this: I divided the cube into three layers (starting with blue, out of habit) and for each one I started from the inside and worked my way out, from 2 coloured pieces to 5 coloured. I would first move all the relevant pieces to the layer I was working on and ensure that they were orientated properly, then I’d move them around on that side to get the right permutation. For the first layer, you can use the method I described above throughout. However, the next two layers force an important restriction on you. If you are using the same algorithms you use in 3D to manipulate pieces on the side in the center of the screen (that’s the -V side), they will also affect all the pieces along the U and V axis with the same XYZ coordinates in the same way. In order to avoid the 3D algorithms affecting the other layers, I used a modified strategy.

Let’s say you’re performing an algorithm on the side you see in the center (-V). You can use your normal 3D algorithms by twisting the surrounding sides (X Y Z). However, this will also affect +V and +-U. So instead of using X Y Z to manipulate the -V side, you restrict yourself to only twisting two opposing sides (say, +-X) When you’d normally twist the Z or Y sides, instead you rotate -V such that you can perform your desired moves using +-X. This will minimalize the effects on the rest of the cube (if anything is messed up, you can fix it by turning one or two sides).

When you get to the 5 coloured pieces, you have to get even more creative, but the strategy I used for them was really just an extension of what I explained (hopefully clearly) above.

I hope I did a decent job of explaining how I went about solving this monster. If anybody has any questions, feel free to ask and I’ll hopefully be able to clarify further.